Critical health- and treatment-related outcomes such as adherence to antiretroviral therapy (number of doses taken out of those prescribed), substance-related problems (e.g., number of problems endorsed), and frailty (e.g., number of Fried Frailty Phenotype criteria experienced) frequently take the form of fractions or proportions. However, fractional and proportional outcomes generally have not been appropriately analyzed in the behavioral HIV field and health outcomes research more broadly, which may lead to invalid conclusions. For example, outcomes such as the proportion of prescribed doses taken are highly skewed with both floor and ceiling effects (i.e., at 0 and 1), which violate the assumptions of commonly used statistical models, such as linear regression. We propose the marginalized zero- and N-inflated binomial (MZNIB) model to assess the overall effects of covariates (e.g., treatment effects) on proportional outcomes. The MZNIB model produces regression estimates that share the familiar interpretation of logistic regression by focusing on the mean probability of the target outcome (e.g., medication adherence) across the entire population. The MZNIB approach provides a more straightforward estimation of an overall effect than traditional zero-inflated models or other alternatives, which produce multiple sets of estimates on fractional outcomes that distinguish, for example, between those who (1) potentially engage in the behavior (e.g., take HIV medication at least occasionally) and (2) never engage in the behavior. In clinical research, it is critical to quantify the overall effect as a benchmark to compare effects, identify reasons for heterogeneity in effects, and improve on effects. Lack of appropriate methods, especially for HIV research, remains a barrier to innovative treatment development and evaluation. To address this gap, this R21 study has three aims: (1) provide best practice recommendations via simulation study regarding when and how the MZNIB model would be preferred over existing approaches for evaluating medication adherence and other proportional outcomes with floor and ceiling effects, (2) produce tutorials for implementing the MZNIB approach to estimate effects of treatment and other predictors using real data from three HIV intervention/prevention trials and a large-scale HIV cohort study (Ns = {70, 73, 224, 9336}), and (3) develop and disseminate the first-ever open-source computational tool for the MZNIB model. This R21 study leverages an established research group with combined expertise in HIV, substance use, and frailty. Findings from this study will empower behavioral HIV research communities by introducing novel statistical models and explaining their assumptions, advantages, and disadvantages in one coherent analytic framework. Simulation studies, accessible tutorials, and substantive application papers that address fractional count outcomes will improve statistical inference and scientific rigor. In additi...